IA. Empirical Research Questions Interpreting Regression Results: A randomly sel
ID: 3228124 • Letter: I
Question
IA. Empirical Research Questions Interpreting Regression Results: A randomly selected one out of following 3 questions will appear on the exam for you to answer All questions will remain the same in content and structure, but variables in the regression and/or specific numbers may change for the final exam. Use the regression equation and table of results below to answer questions 1-3 below. The dependent variable is the average 4th-grade test score for a school district, where the test is measured in points out of 800. The independent variable STR refers to the student-teacher ratio in elementary schools in the district (i.e., the number of students per teacher, which on average is about 20). Non-English is the percent of non-native english speakers attending elementary schools in the district which on average is about 0.16. Free Lunch is the percent of elementary school student who are eligible for free lunch in the district, which on average is about 0.25. The variable ln(Avg Income is the natural logarithm of the average income in the district. Score Bo B STR B20 Free Lunch Buin(Avg Income Ei Non-English) Table 1: Dependent variable 3Average Test Score in the District OLS Student-Teacher Ratio -0.73 (0.26) Percent Non-Native English Speakers 1.76 (0.34) Percent Eligible for Free Lunch -3.98 (0.33) In(Average District Income) 11.57 658.6 Intercept (8.6) Observations 420 0.73 Table Notes: The regression is ordinary Least Squares. Standard errors are in parentheses below each coefficient estimate.Explanation / Answer
1) For every one percentage point increase in the no. of students eligible for free lunch, the average district test score decreases by 3.98. To find if it is statistically significant, first can find the t statistic by dividing the coefficent value by the standard error value
So t = -3.98/0.33 = -12.06061. And p value corresponding to -12.06 is approximately 0. So this effect is statistically significant
2) On increasing the student teacher ratio by 10, the average district test score decreases by (0.73)*10 = 7.3. To find if it is statistically significant, first can find the t statistic by dividing the coefficent value by the standard error value
So t = -0.73/0.26 = -2.807692. And p value corresponding to -2.807692 is approximately 0.00249 = 0.0025 approx. As it is less than 0.05, this effect is statistically significant.
3) For every one unit increase in log value of average district income, the average district test score increases by 11.57. To find if it is statistically significant, first can find the t statistic by dividing the coefficent value by the standard error value
So t = 11.57/1.81 = 6.392265. And p value corresponding to 6.392265 is approximately zero. As it is less than 0.05, this effect is statistically significant.